{
  "id": "2002.04273",
  "version": "v1",
  "published": "2020-02-11T09:23:03.000Z",
  "updated": "2020-02-11T09:23:03.000Z",
  "title": "Linking over cones for the Neumann Fractional $p-$Laplacian",
  "authors": [
    "Dimitri Mugnai",
    "Edoardo Proietti Lippi"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider nonlinear problems governed by the fractional $p-$Laplacian in presence of nonlocal Neumann boundary conditions. We face two problems. First: the $p-$superlinear term may not satisfy the Ambrosetti-Rabinowitz condition. Second, and more important: although the topological structure of the underlying functional reminds the one of the linking theorem, the nonlocal nature of the associated eigenfunctions prevents the use of such a classical theorem. For these reasons, we are led to adopt another approach, relying on the notion of linking over cones.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-11T09:23:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15",
      "47J30",
      "35S15",
      "47G10",
      "45G05"
    ],
    "keywords": [
      "neumann fractional",
      "nonlocal neumann boundary conditions",
      "nonlinear problems",
      "superlinear term",
      "ambrosetti-rabinowitz condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}